August 22, 2012 Subject:
Extract from the preface:
My aim is to exhibit the close connexion between analysis and its applications and, without loss of rigour and precision, to give due credit to intuition as the source of mathematical truth. … To me it seems extremely important that the student should be warned from the very beginning against a smug and presumptuous purism; this is not the least of my purposes in writing this book.
The book is intended for anyone who, having passed through an ordinary course of school mathematics, wishes to apply himself to the study of mathematics or its applications to science and engineering, no matter whether he is a student of a university or technical college, a teacher, or an engineer. I do not promise to save the reader the trouble of thinking, but I do seek to lead the way straight to useful knowledge, and aim at making the subject easier to grasp, not only by giving proofs step by step, but also by throwing light on the interconnexions and purposes of the whole.
The beginner should note that I have avoided blocking the entrance to the concrete facts of the differential and integral calculus by discussions of fundamental matters, for which he is not yet ready. Instead, these are collected in appendices to the chapters …. The reader will notice, too, that the general style of presentation, at first detailed, is more condensed towards the end of the book. He should not, however let himself be disheartened by isolated difficulties which he may find in the concluding chapters. Such gaps in understanding, if not too frequent, usually fill up of their own accord. [And Mr Courant says in Vol. II that students are not expected to read a book like this sequentially.]
[See the preface for some useful remarks on the difference between this and the original German edition.]